Giovanni Landi
Projective Modules of Finite Type over the Supersphere $S^{2,2}
(51K, latex 2e)
ABSTRACT. In the spirit of noncommutative geometry we construct all inequivalent
vector bundles over the $(2,2)$-dimensional supersphere $S^{2,2}$ by
means of global projectors $p$ via equivariant maps. Each projector
determines the projective module of finite type of sections of the
corresponding `rank $1$' supervector bundle over $S^{2,2}$.
The canonical connection $\nabla = p \circ d$ is used to compute the
Chern numbers by means of the Berezin integral on $S^{2,2}$.
The associated connection $1$-forms are graded extensions of monopoles
with not trivial topological charge.
Supertransposed projectors gives opposite values for the charges.
We also comment on the $K$-theory of $S^{2,2}$.